The left face of a biconvex lens has a radius of curvature of magnitude 12.8 cm, and the right face has a radius of curvature of magnitude 17.9 cm. The index of refraction of the glass is 1.45
a) Calculate the focal length of the lens for light incident from the left.
b) After the lens is turned around to interchange the radii of curvature of the two faces, calculate the focal length of the lens for light incident from the left.
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To calculate the focal length of a biconvex lens, we can use the lens maker's formula:
1/f = (n - 1) * [(1/R1) - (1/R2)]
Where:
f is the focal length
n is the refractive index of the material
R1 is the radius of curvature of the left face
R2 is the radius of curvature of the right face
a) For light incident from the left:
R1 = 12.8 cm
R2 = 17.9 cm
n = 1.45
Substituting these values into the lens maker's formula, we get:
1/f = (1.45 - 1) * [(1/12.8) - (1/17.9)]
Simplifying the equation:
1/f = 0.45 * [(17.9 - 12.8)/(12.8 * 17.9)]
Now evaluate the expression in brackets:
1/f = 0.45 * (5.1 / 230.72)
Performing the division and multiplication:
1/f = 0.45 * 0.02213
Calculating the right side of the equation:
1/f = 0.00996
Taking the reciprocal of both sides:
f = 1 / 0.00996
Thus, the focal length of the lens for light incident from the left is approximately 100.4 cm.
b) After the lens is turned around:
Now interchange the radii of curvature:
R1 = 17.9 cm
R2 = 12.8 cm
Using the same formula, we get:
1/f = (1.45 - 1) * [(1/17.9) - (1/12.8)]
Simplifying the equation:
1/f = 0.45 * [(12.8 - 17.9)/(17.9 * 12.8)]
Now evaluate the expression in brackets:
1/f = 0.45 * (-5.1 / 229.12)
Performing the division and multiplication:
1/f = 0.45 * -0.02228
Calculating the right side of the equation:
1/f = -0.00998
Taking the reciprocal of both sides:
f = 1 / -0.00998
Thus, the focal length of the lens for light incident from the left after interchanging the radii of curvature is approximately -100.2 cm.
Note: The negative sign indicates that the lens has a negative focal length, which means the lens is a diverging lens.